This document relates to signal conversion.
A/D converters are devices which convert continuous analog values into a discrete time, digital representation. Some of the most commonly used conventional A/D converters are Flash A/D converters, successive approximation A/D converters, and Sigma-Delta A/D converters. Such A/D converters generally implement a fixed architecture which is designed to work in a broad number of scenarios. The result of using such architectures can be sub-optimal performance in certain scenarios.
For example, using a Flash A/D converter to quantize a signal which does not utilize the full dynamic range of the A/D converter can under-utilize the resolution of the A/D converter. This is due to the architecture of the Flash A/D converter. In particular, Flash A/D converters quantize samples by generating a thermometer code by comparing an analog signal level to a number of fixed reference levels. If there are 255 fixed reference levels and the analog signal levels only vary between reference levels 200 and 250, the result of comparing the other reference levels (i.e., 1-199 and 251-255) to the analog signal level is likely the same from sample to sample.
Sigma-Delta A/D converters generally processes an analog input signal to produce a bit-stream (i.e., a one-bit resolution discrete time signal) that is then digitally filtered and decimated to yield a desired digitized (i.e., multibit discrete time) representation of the input. One form of digital filtering used with Sigma-Delta converters is linear low-pass filtering. A number of techniques have applied non-linear filtering techniques to the bitstream output of an Sigma-Delta converter.
The first is the Zoomer algorithm [S. Hein and A. Zakhor, “New properties of Sigma Delta modulators with DC inputs,” IEEE Transactions on Communications, volume 40, number 8, pp. 1375-1387, August 1992.] Generally, this algorithm assumes a constant input signal and seeks to determine its value by using the bitstream to form upper and lower bounds on the signal that become consistently tighter. This method can performs poorly when the input is not exactly constant (for example, small amounts of additive noise). As few signals are exactly constant and noise free, the Zoomer algorithm is rarely used in practice.
Bandlimited inputs can be nonlinearly decoded from a sigma-delta bitstream using the algorithms of Thao and Vetterly [N. T. Thao and M. Vetterli, “Deterministic analysis of oversampled A/D conversion and decoding improvement based on consistent estimates,” IEEE Transactions on Signal Processing, Volume 42, Issue 3, pp. 519-531, March 1994.]. In this case, alternating projections are used to recover the input by alternating the enforcement of the bandlimited constraint and a constraint that it be consistent with the observed sigma-delta bitstream. The computational complexity of such reconstruction is moderate.
A general reference for known nonlinear decoders is: “Sigma Delta modulators: nonlinear decoding algorithms and stability analysis” by Søren Hein, Avideh Zakhor.